Quasi-optimal degree distribution for a quadratic programming problem arising from the pp-version finite element method for a one-dimensional obstacle problem

We present a quadratic programming problem arising from the pp-version for a finite element method with an obstacle condition prescribed in Gauss–Lobatto points. We show convergence of the approximate solution to the exact solution in the energy norm. We show an a-priori error estimate and derive an a-posteriori error estimate based on bubble functions which is used in an adaptive pp-version. Numerical examples show the superiority of the pp-version compared with the hh-version.